I recently started a sugar cane farm, and I'm just curious as to the rate at which sugar cane grows.
I have an automatic piston-harvested farm with 16 cane plants harvested every ~10 seconds. Here are two different estimations of the rate. By "growth" I mean the event of one block being added to the top of a sugar cane plant.
The latter figure is probably closer to correct as it does not involve an estimation of probability.
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Sugar cane grows using block ticks. Every 16 block ticks it grows, and each block tick happens on average every 68 seconds, that means on average a sugar cane will grow every 1088 seconds, or 18 minutes 8 seconds. This is only with optimal conditions however. Watch all of Wubbi's video, it's really helpful and accurate.